Quantum control based on solid-state nuclear magnetic resonance and its applications

Zhao Liqiang; Li Yuchen; Yin Haochuan; Zhang Shengyu; Wu Ze; Peng Xinhua

doi:10.7498/aps.74.20241709

Abstract
As an important technique for the characterization of materials, solid-state NMR has been widely used in many fields such as physics, materials science, chemistry and biology. In recent years, solid-state NMR has gradually shown important research value and application potential in cutting-edge quantum technologies due to the abundant many-body interactions and pulse control methods. In this paper, we systematically introduce the research objects and theoretical foundations of solid-state NMR, including important nuclear spin interaction mechanisms and their Hamiltonian forms. We also introduce typical dynamical control methods of solid-state nuclear spins, such as such as dynamical decoupling and magic-angle spinning. Furthermore, we focus on recent advancements in the quantum control based on solid-state NMR, including nuclear spin polarization enhancement techniques and the control techniques of Floquet average Hamiltonians. Finally, by presenting some important research works, we discuss the applications of solid-state NMR quantum control technologies in the field of quantum simulation.

Keywords:
Solid-state NMR /

Quantum control /

Nuclear spin interactions /

Quantum simulation
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图 1 (a) 金刚烷样品分子示意图. (b) 氟磷灰石样品原子排布示意图

Figure 1. (a) Schematic diagram of adamantane molecule. (b) Schematic diagram of the atomic configuration of a fluoroapatite sample

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图 2 交叉极化的脉冲序列图.　(a) HHCP; (b) DOCP; (c) ADCP; (d) AD/DO-CP

Figure 2. Pulse sequences of cross polarization. (a) HHCP; (b) DOCP; (c) ADCP; (d) AD/DO-CP

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图 3 16脉冲序列

Figure 3. 16-pulse sequence

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图 4 Magic echo序列

Figure 4. Magic echo sequence

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图 5 WAHUHA序列

Figure 5. WAHUHA sequence

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图 6 魔角旋转示意图

Figure 6. Schematic diagram of magic angle spinning

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图 7 魔角旋转条件下的偶极恢复脉冲序列^[44]

Figure 7. Pulse sequence of dipolar recovery at the magic angle

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图 8 测量多量子相干的脉冲序列

Figure 8. Pulse sequence for measurement of multiple quantum coherences

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表 1 利用8脉冲序列实现不同目标哈密顿量所对应的脉冲欧拉角设置

Table 1. Setup of the Euler angles of 8-pulse sequences for realizing different target Hamiltonians

$ \hat{H}_{\rm tar} $	C	单位(π), $ n=1, 2, 3, 4 $
$ \displaystyle\sum_{i<j}J_{ij}[2\hat{I}^i_z\hat{I}^j_z-\hat{I}^i_x\hat{I}^j_x-\hat{I}^i_y\hat{I}^j_y] $	1	$ \beta_{n}=1, \gamma_n=\dfrac{(n-1)}{2} $
	–0.5	$ \beta_{n}=\dfrac{1}{2}, \gamma_n=\dfrac{(n-1)}{2} $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_x\hat{I}^j_x-\hat{I}^i_y\hat{I}^j_y] $	1	$ \beta_{n}=0.304, \gamma_n=\dfrac{1+4(-1)^n}{4} $
	–1	$ \beta_{n}=0.304, \gamma_n=\dfrac{3+4(-1)^n}{4} $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_z\hat{I}^j_x+\hat{I}^i_x\hat{I}^j_z] $	$ \dfrac{1}{3} $	$ \beta_{n}=0.304, \gamma_n=\dfrac{3(-1)^n}{4} $
	$ \dfrac{-1}{3} $	$ \beta_{n}=0.304, \gamma_n=\dfrac{(-1)^n}{4} $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_z\hat{I}^j_y+\hat{I}^i_y\hat{I}^j_z] $	$ \dfrac{1}{3} $	$ \beta_{n}=0.304, \gamma_n=\dfrac{2+(-1)^n}{4} $
	$ \dfrac{-1}{3} $	$ \beta_{n}=0.304, \gamma_n=\dfrac{2+(-1)^n}{-4} $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_y\hat{I}^j_x+\hat{I}^i_x\hat{I}^j_y] $	1	$ \beta_{n}=0.304, \gamma_n=\dfrac{1+(-1)^n}{2} $
	–1	$ \beta_{n}=0.304, \gamma_n=\dfrac{2+(-1)^n}{2} $

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